64,386 research outputs found
Uniform discretizations: a quantization procedure for totally constrained systems including gravity
We present a new method for the quantization of totally constrained systems
including general relativity. The method consists in constructing discretized
theories that have a well defined and controlled continuum limit. The discrete
theories are constraint-free and can be readily quantized. This provides a
framework where one can introduce a relational notion of time and that
nevertheless approximates in a well defined fashion the theory of interest. The
method is equivalent to the group averaging procedure for many systems where
the latter makes sense and provides a generalization otherwise. In the
continuum limit it can be shown to contain, under certain assumptions, the
``master constraint'' of the ``Phoenix project''. It also provides a
correspondence principle with the classical theory that does not require to
consider the semiclassical limit.Comment: 4 pages, Revte
The probability distribution of the number of electron-positron pairs produced in a uniform electric field
The probability-generating function of the number of electron-positron pairs
produced in a uniform electric field is constructed. The mean and variance of
the numbers of pairs are calculated, and analytical expressions for the
probability of low numbers of electron-positron pairs are given. A recursive
formula is derived for evaluating the probability of any number of pairs. In
electric fields of supercritical strength |eE| > \pi m^2/ \ln 2, where e is the
electron charge, E is the electric field, and m is the electron mass, a
branch-point singularity of the probability-generating function penetrates the
unit circle |z| = 1, which leads to the asymptotic divergence of the cumulative
probability. This divergence indicates a failure of the continuum limit
approximation. In the continuum limit and for any field strength, the positive
definiteness of the probability is violated in the tail of the distribution.
Analyticity, convergence, and positive definiteness are restored upon the
summation over discrete levels of electrons in the normalization volume.
Numerical examples illustrating the field strength dependence of the asymptotic
behavior of the probability distribution are presented.Comment: 7 pages, REVTeX, 4 figures; new references added; a short version of
this e-print has appeared in PR
Analytic Results in 2D Causal Dynamical Triangulations: A Review
We describe the motivation behind the recent formulation of a nonperturbative
path integral for Lorentzian quantum gravity defined through Causal Dynamical
Triangulations (CDT). In the case of two dimensions the model is analytically
solvable, leading to a genuine continuum theory of quantum gravity whose ground
state describes a two-dimensional "universe" completely governed by quantum
fluctuations. One observes that two-dimensional Lorentzian and Euclidean
quantum gravity are distinct. In the second part of the review we address the
question of how to incorporate a sum over space-time topologies in the
gravitational path integral. It is shown that, provided suitable causality
restrictions are imposed on the path integral histories, there exists a
well-defined nonperturbative gravitational path integral including an explicit
sum over topologies in the setting of CDT. A complete analytical solution of
the quantum continuum dynamics is obtained uniquely by means of a double
scaling limit. We show that in the continuum limit there is a finite density of
infinitesimal wormholes. Remarkably, the presence of wormholes leads to a
decrease in the effective cosmological constant, reminiscent of the suppression
mechanism considered by Coleman and others in the context of a Euclidean path
integral formulation of four-dimensional quantum gravity in the continuum. In
the last part of the review universality and certain generalizations of the
original model are discussed, providing additional evidence that CDT define a
genuine continuum theory of two-dimensional Lorentzian quantum gravity.Comment: 66 pages, 17 figures. Based on the author's thesis for the Master of
Science in Theoretical Physics, supervised by R. Loll and co-supervised by J.
Ambjorn, J. Jersak, July 200
Doublet structures in quantum well absorption spectra due to Fano-related interference
In this theoretical investigation we predict an unusual interaction between a
discrete state and a continuum of states, which is closely related to the case
of Fano-interference. It occurs in a GaAs/AlxGa1-xAs quantum well between the
lowest light-hole exciton and the continuum of the second heavy-hole exciton.
Unlike the typical case for Fano-resonance, the discrete state here is outside
the continuum; we use uniaxial stress to tune its position with respect to the
onset of the continuum. State-of-the art calculations of absorption spectra
show that as the discrete state approaches the continuum, a doublet structure
forms which reveals anticrossing behaviour. The minimum separation energy of
the anticrossing depends characteristically on the well width and is unusually
large for narrow wells. This offers striking evidence for the strong underlying
valence-band mixing. Moreover, it proves that previous explanations of similar
doublets in experimental data, employing simple two-state models, are
incomplete.Comment: 21 pages, 5 figures and 5 equations. Accepted for publication in
Physical Review
Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality
We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial
three-torus. The low energy spectrum consists of a number of continua of states
of arbitrarily low energies. Although the theory has no mass-gap, it appears
that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes
of the continua are computable in a semi-classical approximation. The
wave-functions of the low-energy states are supported on submanifolds of the
moduli space of flat connections, at which various subgroups of the gauge group
are left unbroken. The field theory degrees of freedom transverse to such a
submanifold are approximated by supersymmetric matrix quantum mechanics with 16
supercharges, based on the semi-simple part of this unbroken group. Conjectures
about the number of normalizable bound states at threshold in the latter theory
play a crucial role in our analysis. In this way, we compute the low-energy
spectra in the cases where the simply connected cover of the gauge group is
given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of
S-duality are obeyed for unique values of the number of bound states in the
matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the
proof involves surprisingly subtle combinatorial identities, which hint at a
rich underlying structure.Comment: 28 pages. v2:reference adde
Peculiar properties of the cluster-cluster interaction induced by the Pauli exclusion principle
Role of the Pauli principle in the formation of both the discrete spectrum
and multi-channel states of the binary nuclear systems composed of clusters is
studied in the Algebraic Version of the resonating-group method. Solutions of
the Hill-Wheeler equations in the discrete representation of a complete basis
of the Pauli-allowed states are discussed for 4He+n, 3H+3H, and 4He+4He binary
systems. An exact treatment of the antisymmetrization effects are shown to
result in either an effective repulsion of the clusters, or their effective
attraction. It also yields a change in the intensity of the centrifugal
potential. Both factors significantly affect the scattering phase behavior.
Special attention is paid to the multi-channel cluster structure 6He+6He as
well as to the difficulties arising in the case when the two clustering
configurations, 6He+6He and 4He+8He, are taken into account simultaneously. In
the latter case the Pauli principle, even in the absence of a potential energy
of the cluster-cluster interaction, leads to the inelastic processes and
secures an existence of both the bound state and resonance in the 12Be compound
nucleus.Comment: 17 pages, 14 figures, 1 table; submitted to Phys.Rev.C Keywords:
light neutron-rich nuclei, cluster model
The quantum auxiliary linear problem & Darboux-Backlund transformations
We explore the notion of the quantum auxiliary linear problem and the
associated problem of quantum Backlund transformations (BT). In this context we
systematically construct the analogue of the classical formula that provides
the whole hierarchy of the time components of Lax pairs at the quantum level
for both closed and open integrable lattice models. The generic time evolution
operator formula is particularly interesting and novel at the quantum level
when dealing with systems with open boundary conditions. In the same frame we
show that the reflection K-matrix can also be viewed as a particular type of
BT, fixed at the boundaries of the system. The q-oscillator (q-boson) model, a
variant of the Ablowitz-Ladik model, is then employed as a paradigm to
illustrate the method. Particular emphasis is given to the time part of the
quantum BT as possible connections and applications to the problem of quantum
quenches as well as the time evolution of local quantum impurities are evident.
A discussion on the use of Bethe states as well as coherent states and the path
integral formulation for the study of the time evolution is also presented.Comment: 20 pages Latex. Contribution to the proceedings of the Corfu Summer
Institute 2019 "School and Workshops on Elementary Particle Physics and
Gravity", 31 August - 25 September 201
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